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For a cylindrical pressure r1 ¼ 1; r2 ¼ R, which gives pR 2 vessel ð5:10Þ of radius R, we have pR 2 ð5:11Þ N ¼ pR ð5:12Þ N ¼ Copyright 2005 by CRC Press, Inc. All Rights Reserved. This gives the hoop stress hoop ¼  ¼ N pR ¼ t t ð5:13Þ long ¼  ¼ N pR ¼ 2t t ð5:14Þ and the longitudinal stress These results will be shown to be identical to the results that follow. Let us consider a long thin cylindrical shell of radius R and thickness t, subject to an internal pressure p. By thin shells we mean the ones having the ratio R/t typically greater than about 10.

18) may be used to define domains of applicability of various stress limits. The interaction curves based on exact methods using Appendix B and those using Eq. 7 for the circular and diamond sections. The exact and the approximate solutions are not too different from each other. For sections that are not full, the above approximations to the interaction curves cannot be used, and each point on the interaction curve has to be obtained explicitly. For such sections, Eq. 18) is replaced with y ¼ when x ¼ 0; ð4:19Þ The value of has to be evaluated numerically.

3. L. Three-dimensional stress criteria – summary of the PVRC project, J. , 122, 105–109, 2000. 4. , Allowable stresses for nonrectangular sections under combined axial and bending loads, J. , 110, 188–193, 1988. 5. , Wiley, New York, 1952. 6. , Plastic Analysis of Structures, McGraw-Hill, New York, 1959. Problems 1. Determine the interaction curve for a thin-walled I-beam of height h and width h/2 and having a wall thickness of t (t<

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